The graph shows a line and two similar triangles. On a coordinate plane, a line goes through (0, 0) and (8, 2). A small triangle has a rise of 1 and run of 4, and a larger triangle has a rise of 2 and run of 8. Which expression finds the equation of the line? StartFraction y Over x EndFraction = one-fourth StartFraction y Over 4 EndFraction = StartFraction x Over 1 EndFraction StartFraction y Over x EndFraction = StartFraction 4 Over 1 EndFraction StartFraction y Over 1 EndFraction = StartFraction 4 Over x EndFraction

From the two column proof below, we have seen ∠BAC ≅ ∠DAC by CPCTC

The two column proof to show that ∠BAC ≅ ∠DAC is as follows:

Statement 1: ΔABD is Isosceles with base BD, AC ⊥ BD

Reason 1: Given

Statement 2: AB ≅ AD

Reason 2:  Definition of isosceles Triangles

Statement 3: ∠1 and ∠2 are right angles

Reason 3: Definition of perpendicular

Statement 4: AC ≅ AC

Reason 4: Reflexive Property

Statement 5: ΔABC and ΔADC are right triangles

Reason 5: Definition of right triangle

Statement 6: ΔABC ≅ ΔADC

Reason 6: HL Congruency

Statement 7: ∠BAC ≅ ∠DAC

Reason 7: CPCTC

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Answer:

answer down below

Step-by-step explanation:

1.A+B=61

2.41+25=61

The restricted domain of the function is 0≤s≤25

The equation is a(s) = 37.5s - 1.5s²  models the function represented in the table

a(s) = s(37.5 - 1.5s)

The critical points are s=0 or

37.5 - 1.5s

37.5 = 1.5s

s=25

As area can not be negative, the area should be positive

s< 0 and s>25

Therefore, restricted domain is 0≤s≤25

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Answers:

You may or may not have to type in the word "degrees", and/or use the degree symbol. I would ask your teacher for clarification.

A diagram is shown below.

============================================================

Explanation:

We'll need the law of cosines to solve for angle A.

a^2 = b^2 + c^2 - 2*b*c*cos(A)

17^2 = 36^2 + 45^2 - 2*36*45*cos(A)

289 = 3321 - 3240*cos(A)

289 - 3321  = -3240*cos(A)

-3032  = -3240*cos(A)

-3240*cos(A) = -3032

cos(A) = (-3032)/(-3240)

cos(A) = 0.935802

A = arccos(0.935802)

A = 20.64 degrees

which is approximate to 2 decimal places.

Note: The "arccos" refers to "arccosine" which is the same as inverse cosine (denoted as \(\cos^{-1}\) on many calculators).

-----------------------------

Do a similar set of steps for angle B.

b^2 = a^2 + c^2 - 2*a*c*cos(B)

36^2 = 17^2 + 45^2 - 2*17*45*cos(B)

1296 = 2314 - 1530*cos(B)

1296 - 2314  = -1530*cos(B)

-1018  = -1530*cos(B)

-1530*cos(B) = -1018

cos(B) = (-1018)/(-1530)

cos(B) = 0.665359

B = arccos(0.665359)

B = 48.29 degrees

Also approximate to 2 decimal places.

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As you can probably guess by now, we could use the law of cosines to find angle C. But a much quicker shortcut is to use the fact that for any triangle, the interior angles always add to 180 degrees.

This shortcut is only possible since we know the two other angles.

Solve for C.

A+B+C = 180

C = 180-A-B

C = 180 - 20.64 - 48.29

C = 111.07 degrees

Like the others, this is approximate to 2 decimal places.

You can use a graphing tool like GeoGebra to confirm the answers. See below. Due to the SSS (side side side) triangle congruence theorem, only one triangle is possible. This means only one answer is possible per angle.

Answer:

D. 2

Step-by-step explanation:

A degree of a polynomial is the highest exponent. In this case, it is 2 because 2x is being squared.

Option D is correct, 2 is the degree of the polynomial  2x²+3x+1.

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given expression is  2x²+3x+1

In words two times of x square plus three times of x plus one.

x is the variable in the given expression or polynomial.

Plus is the operator.

The degree of a polynomial is the highest power of the variable in the polynomial.

In the expression 2x²+3x+1, the highest power of the variable is 2, so the degree of the polynomial is 2.

Hence, 2 is the degree of the polynomial  2x²+3x+1.

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Answer: shifted by  3*pi/2 units to the right.

Step-by-step explanation:

Here we have:

y = sin(x - 3*pi/2)

now, you need to remember this:

if we have y = f(x)

then y' = f(x - A) is the graph of y, shifted A units to the right (where A is a positive number).

If A is negative, the shift is to the left.

Then in this case, we have:

sin(x) -----> sin( x - 3*pi/2)

A = 3*pi/2

Then we have the graph shifted by  3*pi/2 units to the right.

Answer:

C. 3pi/2 units to the right

Step-by-step explanation:

(I got it right on edge)

Answer:

5x+7 > 17 matches with 3.

1+3x > -5 matches with 2.

2x+1 < 3 matches with 1.

5-3x > 11 matches with 4.

Step-by-step explanation:

Answer:

To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced.

So x = 10

Explanation:

Given the below equation;

To isolate the variable, we have to add 3 to both sides of the equation to keep the equation balanced;

Answer:

Hey

Step-by-step explanation:

Write the fraction in simplest form

\( - \frac{29}{18} \)

\( \frac{8}{9} - \frac{5}{2} \)

Find the difference between 8/9 and 5/-2

\( \frac{8}{9} - \frac{5}{2} \)

\( \frac{8 \times 2}{9 \times 2} - \frac{5 \times 9}{2 \times 9} \)

\( \frac{16}{18} - \frac{45}{18} \)

\( \frac{16 - 45}{18} \)

\( \frac{ - 29}{18} \)

\( - \frac{29}{18} \)

The simplified expression of the given expression is 4√2

From the question, we have the following parameters that can be used in our computation:

√32

Express 32 as 16 * 2

So, we have

√32 = √16 * √2

Evaluate the radicand

√32 = 4√2

HEnce, the solution is 4√2

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The value of x for the equation to have infinite solution is 12

For an equation to have infinite solution, the expression on both sides must be equal

Given the expression below

3x–18=3(x–10)+ x

expand

3x - 18 = 3x - 30 + x

Equate

-18 = -30 + x

x = -18 + 30

x = 12

Hence the value of x for the equation to have infinite solution is 12

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Answer:

Hello, the Answer is 132

Hope this helped:)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Round both numbers to the nearest tens place.

98.7 rounds up to 100

10.1 rounds down to 10

100/10=10

Answer: 18(a)-89=217

Step-by-step explanation:

If a = 17 then you substitute/replace the a with the 17. Making 18(a) into 18(17). 18(17)= 306 - 89 = 217.

Hope this helped.

Answer:217

Step-by-step explanation:

putting the value of a in the equation.

18×17-89= 217

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer: C

Step-by-step explanation:

Point D is at -14 on the number line.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since E is the midpoint of line segment CD, we can logically deduce the following relationship:

Line segment CD = Line segment C + Line segment D

Midpoint E = (point C + point D)/2

By substituting the given points into the equation above, we have the following:

-3 = (8 + D)/2

-6 = 8 + D

D = -6 - 8

D = -14

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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Answer:

A=4 B=1 C=2 D=5 E=3

Step-by-step explanation:

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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Answer:

a

Step-by-step explanation:

The hybrid SUV uses 32/55 gallons per hour which is the correct answer would be an option (A).

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.

The operator that perform the arithmetic operations are called arithmetic operators.

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

Given that a hybrid SUV gets 32miles per gallon on the highway driving at a constant 55 miles per hour

To determine miles per gallon of gas,

We take the 32miles the hybrid SUV travels and divide it by the highway driving at a constant 55 miles per hour

⇒ 32/55

Hence, the hybrid SUV uses 32/55 gallons per hour.

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Answer: x=3\(\sqrt{2\). y=3\(\sqrt{2\)

Step-by-step explanation: This is a 45-45-90 triangle. Both of the legs, x and y, are congruent. To find the length of the legs, divide 6, the hypotenuse, by \(\sqrt{2\). 6/\(\sqrt{2\)=3\(\sqrt{2\).

Answer:

36.3636364%

or 36.36

Step-by-step explanation:

Answer:

false

Step-by-step explanation:

Credit Unions are not-for-profit financial service cooperatives

Answer: 38

Step-by-step explanation:

61/3 divided by 1/3

Answer:

Negative 5

Step-by-step explanation:

\(10x+5-5=9x-5\)

\(10x+5-5\\= 10x+\left(5-5\right)\\= 5-5\\=0\\=10x+0\\=10x\)

--------------

\(9x-5\\= 9x-5\)

→ \(10x=9x-5\)

\(10x-9x=9x-5-9x\)

\(10x - 9x\\= 1x\\= 1 \times x\\= 1\)

\(9x-5-9x\\=9x\left(-5\right)-9x\\= 9x - 9x\\= 0 - \left(-5\right)\\= -5\\x = -5\)

Hope this helps!